•Method 2: Non-explicit traces (Kronecker deltas, f's and d's)

llle = ExpandU[lll] // Simplify ;

The gauge group is SU( 3 ); the dimension of the representation is 3

Expanding the NM products

Applying expansion rules

Applying CommutatorReduce

$IsoIndicesCounter = 0 ;

$VeryVerbose = 0 ;

llll = llle // IsoIndicesSupply // IndicesCleanup // SUNReduce // Simplify ;

fields = FieldsSet[QuantumField[Particle[PhiMeson, RenormalizationState[0]]]]

{ϕ^( )^I _ 1, ϕ^( )^I _ 2, ϕ^( )^I _ 3, ϕ^( )^I _ 4}

llll // Length

3

llll // Expand // Length

70

res = (WriteString["stdout", "."] ; FeynRule[#, fields]) & /@ Expand[llll] ;

......................................................................

res // Length

332

res // LeafCount

13799

mel = ((WriteString["stdout", "."] ; IndicesCleanup[SUNReduce[#]]) & /@ res) ;

............................................................................................................................................................................................................................................................................................................................................

mel // LeafCount

9039

melsimplified = I * Collect[mel/I, {_ParticleMass, _DecayConstant, _SU3D, _SU3F, _SU3Delta}] ;

melsimplified // LeafCount

4785

Converted by Mathematica  (July 10, 2003)